* Authorities say four al Qaeda men shot dead in capital (Adds four deaths in gunfight in Sanaa)

By Mohammed Mukhashaf

ADEN, Yemen, May 8 (Reuters) - Western embassies in Yemen heightened security on Thursday after increasingly bold attacks on foreigners by al Qaeda, even as the militant Islamists lost ground to an army offensive in the south.

The European Union said on Thursday it had limited its presence in Yemen to essential staff, while France ordered its diplomats to restrict their movement.

"Like other diplomatic and international actors in Sanaa, we are limiting the presence to essential staff and reviewing our security measures," said Michael Mann, a spokesman for EU foreign policy chief Catherine Ashton.

On Wednesday, the United States announced a suspension of operations at its embassy.

Farhan Haq, a spokesman for the United Nations in New York, said the world body had no plans to move out of Yemen.

"To the contrary, (it) is determined to continue the implementation of its critical mandates in this country, including political, development and humanitarian. To enable the above, the U.N. is applying a variety of security risk management options," Haq said without elaborating.

A spokeswoman for France's Foreign Ministry said its security alertness in Yemen was at maximum but the embassy remained open. On Monday, a French security agent was killed in the capital Sanaa.

Britain's Foreign Office issued a new travel alert on Thursday, advising against all travel to Yemen and strongly urging British nationals to leave the Arabian Peninsula state.

The International Committee for the Red Cross, whose staff have been kidnapped and shot in recent years in Yemen, said it was reducing its exposure in Sanaa, where it described the security conditions as "extremely worrying, unpredictable".

"There are no private movements within the country except when people go to the airport for their (breaks)," Robert Mardini, head of ICRC operations for the Near and Middle East, told Reuters in Geneva.

On Wednesday Yemen said its special forces had killed a militant suspected of masterminding attacks on Westerners, including the killing of the French agent on Monday.

Four members of al Qaeda were killed by security services in the capital Sanaa, the Defence Ministry said on its website late on Thursday. It said the men started a gunfight after police stopped their vehicle and tried to detain them.

"LAST STRONGHOLD CAPTURED"

The government's offensive in the south is the most concerted campaign against al Qaeda in the Arabian Peninsula (AQAP) in nearly two years. The group has been blamed for deadly attacks against security forces, foreigners and oil and gas facilities.

Yemen said its forces captured Azzan, the last major militant bastion, in an offensive that began 10 days ago.

The Yemeni defence minister told a crowd celebrating the capture of the town that the army's offensive against AQAP would continue, the state news agency Saba said.

Azzan, with a population of about 50,000, and other towns in the south were declared Islamic emirates in 2011 by Ansar al-Sharia, an AQAP affiliate.

The army drove them out in 2012 but the militants then rebuilt their presence, exploiting the central government's traditionally weak hold over the region.

"We hope that the entrance of the army and the return of state authority to Azzan and other areas will be the end of the worry and turmoil that we've been living with for years," Azzan resident Mubarak Mahdi said.

Washington is keen to prevent any spillover of violence into neighbouring oil power Saudi Arabia and to stop Yemen being used as a springboard to attack Western targets. (Additional reporting by Mohammed Ghobari in Sanaa; editing by Angus McDowall and Andrew Roche)